عنوان

Ramsey methods in analysis /

0817672648

1281349240

3764372648

3764373601

9780817672645

9781281349248

9783764372644

9783764373603

b713211

Ramsey methods in analysis /

[Book]

Spiros A. Argyros, Stevo Todorcevic.

Boston :

Birkhäuser,

©2005.

1 online resource (257 pages) :

illustrations

Advanced courses in mathematics, CRM Barcelona

Includes bibliographical references (pages 247-252) and index.

Saturated and Conditional Structures in Banach Spaces -- Tsirelson and Mixed Tsirelson Spaces -- Tree Complete Extensions of a Ground Norm -- Hereditarily Indecomposable Extensions with a Schauder Basis -- The Space of the Operators for Hereditarily Indecomposable Banach Spaces -- Examples of Hereditarily Indecomposable Extensions -- The Space $$\mathfrak{X}\omega _1 $$ -- The Finite Representability of $$J_{T_0 }$$ and the Diagonal Space $$D \left({\mathfrak{X}_\gamma } \right)$$ -- The Spaces of Operators $$L\left({\mathfrak{X}_\gamma } \right)$$, $$L\left({X, \mathfrak{X}\omega _1 } \right)$$ -- Transfinite Schauder Basic Sequences -- The Proof of the Finite Representability of $$J_{T_0 }$$ -- High-Dimensional Ramsey Theory and Banach Space Geometry -- Finite-Dimensional Ramsey Theory: Finite Representability of Banach Spaces -- Ramsey Theory of Finite and Infinite Sequences -- Ramsey Theory of Finite and Infinite Block Sequences -- Approximate and Strategic Ramsey Theory of Banach Spaces.

0

"This book introduces graduate students and researchers to the study of the geometry of Banach spaces using combinatorial methods. The combinatorial, and in particular the Ramsey-theoretic, approach to Banach space theory is not new; it can be traced back as early as the 1970s. Its full appreciation, however, came only during the last decade or so, after some of the most important problems in Banach space theory were solved, such as, for example, the distortion problem, the unconditional basic sequence problem, and the homogeneous space problem. The book covers most of these advances, but one of its primary purposes is to discuss some of the recent advances that are not present in survey articles of these areas. We show, for example, how to introduce a conditional structure to a given Banach space under construction that allows us to essentially prescribe the corresponding space of non-strictly singular operators. We also apply the Nash-Williams theory of fronts and barriers in the study of Cezaro summability and unconditionality present in basic sequences inside a given Banach space. We further provide a detailed exposition of the block-Ramsey theory and its recent deep adjustments relevant to the Banach space theory due to Gowers."--Jacket.

MIL

134924

Ramsey methods in analysis.

Normed linear spaces.

Ramsey theory.

Set theory.

Análise funcional.

Análise funcional.

Geometria de espaços de banach.

Geometria de espaços de banach.

Normed linear spaces.

Normed linear spaces.

Ramsey theory.

Ramsey theory.

Set theory.

Set theory.

MAT037000

PBKF

QA

Argyros, S., (Spiros),1950-

Todorcevic, Stevo.

20201208033910.0

pn

[Book]

Y